Eric The Blue

Recreational math

Scraping around for a birthday present for one of my nephews, a college student majoring in computer science, I picked out a copy of Martin Gardner's My Best Mathematical and Logic Puzzles.  And since I'm pretty geeky myself, I couldn't help scanning it before the time came to wrap it in paper.  The first problem didn't interest me much.  Here's the second:

Two men play a game of draw poker in the following curious manner.  They spread a deck of 52 cards face up on the table so that they can see all the cards.  The first player draws a hand by picking any five cards he chooses.  The second player does the same.  The first player may now keep his original hand or draw up to five cards.  His discards are put aside out of the game.  The second player may now draw likewise.  The person with the higher hand then wins.  Suits have equal value, so that two flushes tie unless one is made of higher cards.  After a while the players discover that the first player can always win if he draws correctly.  What hand must this be?

That's down my alley.  I think I have an idea of how the first few games might go.  Since an ace-high straight flush is the highest hand in 5-card draw, the first player might in the first game thoughtlessly begin by choosing the ace, king, queen, jack and ten of a certain suit.  You can't lose with that.  But, according to the rules of this eccentric poker game, it quickly becomes evident that you can't win with it, either.  The second player need only choose the same  five cards of one of the other three suits.  It's easy to see how that game ends.  It's a tie.

The problem with the first player's first strategy is that it left the highest possible hand open to the other player.  The first player might prevent that in the second game by choosing, for his first hand, all four aces and one king.  Obviously the ace-high flush is now possible only for player one.  It turns out, however, that the first player's second strategy is worse than his first.  The second player should choose all four queens.  The highest possible hand available to player one is now a jack-high straight flush.  Meanwhile, player two is set up to fill in a queen-high straight flush on his second move.  The only way to prevent it is a defensive move that leaves player one with a hand lower than four queens.  Check mate.  Player two wins.

The way that hand works should, however, suggest a winning strategy to player one.  Picking four tens prevents player one from achieving an ace-high straight flush just as surely as picking four aces did.  Player two can now not make a hand higher than a 9-high straight flush, whereas player one is set up to fill in a 10-high straight flush on his second move.  Trying to block him by choosing four nines doesn't work (because player one, discarding three of his four tens, fills in an ace-high straight flush on his second move; player two cannot achieve a tie as none of the tens are available to him).  Of course, trying to block him by choosing four aces, or four kings or queens or jacks, is also useless (because player one uses his second move to complete a 10-high straight flush, and, as before, the highest hand availabe to player two is a 9-high straight flush). 

Is there something a little off about the wording of the problem?  "What hand must this be?"--makes it sound as if there is only one hand that guarantees victory when actually four tens and any fifth card will do it.  And you know what?  The first player can guarantee victory by choosing just three tens on his first play, but in that case he has to exercise some care in the choice of the other two cards--the jack and the six, for example, from the suit in which he lacks the ten will work.  I'll leave it to my dweeby readers to  work out all the details.

If you find these kinds of problems difficult, here is an interesting conversation that should make you feel better.  Almost everyones' instincts are wrong when it comes to puzzlers of the kind that interest recreational mathematicians and, increasingly, neuroscientists.  Our minds, the product of evolution by natural selection, are built to cope with other challenges.   

I read Power Line so that you don't have to

There's a new look at the Power Line blog but the content is the same old sludge.  In a post entitled "Norway: A Postscript," John Hinderaker begins:

They are still counting the bodies in Norway, and it is probably unseemly to start making political points. . .

The rest of the post makes a political point.  The point is that someone other than the shooter should have had a gun.  This wouldn't happen in South Dakota, where he grew up.  Etc. 

Since I agree with Hinderaker about his unseemliness, let us put that question to the side.  The evidence doesn't support his point.  To say that it wouldn't happen in South Dakota doesn't count for much.  It hadn't happened in Norway until last week.  It was the bloodiest day on Norwegian soil since World War II.  Rates of gun ownership in Norway are not particularly low--a little less than half that of the United States, where the rate of gun violence is on a different order of magnitude.  We have a little more than 50 times the population of Norway and about 2000 times the number of homicides committed with guns.  The homicide rate in Norway is somewhat lower than in South Dakota. 

The "coverage" to which the post calling for more guns is a "postscript" began while the crime was in progress.  Hinderaker:

The perpetrators of these attacks have not yet been identified, but they likely were Muslim terrorists.

When that turned out to be false--well, I should let him speak for himself, since he doesn't allow that it was false:

Was that wrong?  Not at all.  Any time mass murder attacks take place, it is not just likely but highly probable that they are the work of Muslim jihadists.  Over the last several decades, jihadists have launched hundreds if not thousands of terrorist attacks.  They dwarf, in numbers, similar outrages perpetrated by anyone else.

No, wrong.  Either Hinderaker is confused himself or else he's trying to confuse his readers (or maybe just appeal to their prejudices).  The logical connection between the "mass murder" of one sentence and the "hundreds if not thousands of terrorist attacks" of the next is, to put it charitably, weak.  Is he saying that he is justified,  hearing news of mass murder, in concluding that it is likely the work of Muslim jihadists, because there have been "hundreds if not thousands" of mass murders in recent years, almost all committed by Muslims?

Events that do not rise to the level of "mass murder" are used to justify sweeping, and false, generalizations about mass murder.  9/11 was the work of Muslim terrorists.  Oklahoma City was not.  Nor the shootings at Virginia Tech.  Jared Loughner is not a Muslim jihadist.  The sarin attack in the Tokyo subway system was not perpetrated by Muslims.  In "the past several decades" there have been scores of terrorist attacks in northern Ireland, none by Muslim jihadists, who also had nothing to do with the killing of 380 schoolchildren at Beslan, Russia, in 2004.  And this Norwegian crackpot isn't a Muslim terrorist, either. 

Meanwhile, sidekick Johnson takes a feeble swing at James Fallows, whom he charges with "a swarm of foul-mouthed and openly anti-Semitic tweeters."   I take this as a kind of code for stating that Fallows has a dim view of the settlement movement in Israel.  Anyway, judge for yourself.  Rubin.  Fallows. 

  

Bate's Johnson

I've started W. Jackson Bate's biography of Samuel Johnson and am reminded all over again of why I love Dr. Johnson.  Herewith an abbreviated miscellany gleaned either from Bate or my own prior enjoyable researches.

On his youthful reading: "What I read were not voyages and travels, but all literature, sir, all ancient writers, all manly."

On marriage (from Rasselas): "Such is the common process of marriage.  A youth and maiden meeting by chance, or brought together by artifice, exchange glances, reciprocate civilities, go home, and dream of one another.  Having little to divert attention, or diversify thought, they find themselves unhappy when they are apart, and therefore conclude that they shall be happy together.  They marry, and discover what nothing but voluntary blindness had before concealed.  They wear out life in altercations, and charge nature with cruelty."

On second marriages: "The triumph of hope over experience."

From his Life of Milton, in Lives of the Poets: "Paradise Lost is one of the books which the reader admires and puts down, and forgets to take up again.  No one ever wished it longer than it is."

From his review of a theological work wherein the argument is advanced that God, in his infinite mercy, shields the poor from misery by granting them immunity from life's small annoyances: "The poor indeed are insensible of many little vexations which sometimes embitter the possessions and pollute the enjoyment of the rich.  They are not pained by casual incivility, or mortified by the mutilation of a compliment; but this happiness is like that of the malefactor who ceases to feel the cords that bind him when the pincers are tearing his flesh."

In the same review, regarding the author's fantasy that we might better bear our burdens by considering that, to "superior beings," human misery looks no worse than the plight of animals to us, Dr. Johnson, with unconcealed contempt, suggested that the argument could have been carried further: "He might have shown that the hunters whose game is man have many sports analogous to our own.  As we drown whelps and kittens, they amuse themselves now and then with sinking a ship, and stand around the fields of Blenheim or the walls of Prague, as we encircle a cock-pit.  As we shoot a bird flying, they take a man in the midst of his business or pleasure, and knock him down with an apoplexy.  Some of them, perhaps, are virtuosi, and delight in the operations of an asthma, as a human philosopher in the effects of the air pump.  To swell a man with a tympany is as good a sport as to blow a frog.  Many a merry bout have these frolic beings at the vicissitudes of an ague, and good sport it is to see a man tumble with an epilepsy, and revive and tumble again, and all this he knows not why.  As they are wiser and more powerful than we, they have more exquisite diversions, for we have no way of procuring any sport so brisk and so lasting as the paroxysms of the gout and stone which undoubtedly must make high mirth, especially if the play be a little diversified with the blunders and puzzles of the blind and deaf."

Responding to the complaints of the American colonists in his pamphlet, Taxation No Tyranny: "How is it that we hear the loudest yelps for liberty among the drivers of negroes?" 

Offering advice: "My good friend, clear your mind of cant.  You may say to a man, 'Sir, I am your most humble servant.'  You are not his most humble servant.  You tell a man, 'I am sorry you had such bad weather and were so much wet.'  You don't care sixpence whether he is wet or dry.  You talk in this manner; it is a mode of talking in Society: but don't think foolishly."

But such mind droppings are too much the method of Boswell.  Bate, I think, is especially strong on Johnson during his twenties and thirties, two decades during which, out of the eye of biography, he suffered extreme hardships, feared for his sanity, and may have contemplated suicide.  Beckett said that Johnson meant as much to him as any author, which will seem to you very strange if you know Beckett and only Boswell's Johnson.  Bate's Johnson is the one Beckett considered a kindred spirit: "the confident public man," as J.M. Coetzee has written, "who sees no point in living yet cannot face annihilation."

 

 

Our Mutual Friend: I come to the end

I've just finished Our Mutual Friend, the last novel Dickens completed.  The current critical consensus, one gleans from reading here and there, is that the early novels of "the jolly Dickens" were loved by his contemporaries, but that as he aged, and his vision darkened, he produced the works--Bleak House, Little Dorrit, and Our Mutual Friend--on which his reputation as the greatest of the English novelists now rests.  My own eccentric impression is that his vision did not darken to the point that his fiction attained the  crepuscular quality of reality.  I have in mind, for example, the rather too obviously contrasting couples, the Lammles, who marry for money only to discover that he does not have as much as she thought and that she does not have as much as he thought, and the Harmons, who marry only after John proves to himself that Bella knows nothing of his incipient wealth.  She marries him anyway, of course, and gets her reward, while the cold, manipulative Lammles suffer unhappiness before being dismissed from the plot.  It would be pleasant if life were like that.

The scene in which Bella discovers that she has picked, not only a good man but also a rich one, is as we say "over the top" somewhat in the manner of an episode of "Extreme Makeover."  I am not one of those who love Dickens unreservedly. 

Watching movies while the country burns

Here in Minnesota, where Governor Dayton has capitulated to Republicans, accepting their plan to balance the budget without raising any new revenue (by delaying already-delayed payments to public schools and by selling bonds to get money today for money to be received in the future from a tobacco suit settlement), the wingnuts are so crazy that they haven't the sense to declare victory.  Oh, it's a hard deal!  No one likes it!  They have had to give up the dream of passing a budget that restricts access to abortion, shuts down stem cell research, and prevents four felons from voting in one election after another.  Everything related to the budget, they got.

Dayton says that, bad as the deal is, the state government shutdown was worse, and, since Republicans just weren't going to meet him at any middle point, he had to take their offer.  In the realm of theory, it is conceivable that the Republicans would have had to concede that "Governor Dayton just wasn't going to meet us in the middle," and that "we therefore had no choice but to take his offer."  But in the real world, as distinguished from some conceptual one, it helps to be crazy.

Pro-business Republicans are naturally opposed to suing Big Tobacco, but they aren't against using the money from the settlement to run state government, especially if the alternative is a tax hike on people with seven-figure incomes.   

Meanwhile, the national Republicans are showing signs that they are not so crazy as to be blind to their own craziness.  I have in mind Sen. Mitch McConnell's plan to avoid a catastophic default by permitting Obama unilaterally to raise the debt ceiling, then objecting, then permitting Democrats to overcome those objections, then campaigning against Obama and the Democrats for having raised the debt ceiling.  Ingenious! They know what needs to be done.  They just won't do it. 

They're interested in winning elections but not in governing.

It's all sufficiently dreary to cause me to resort to unnatural tactics in the pursuit of relief.  Last night, during negotiations conducted before the menu of Netflix selections eligible for streaming to our TV, I allowed Amanda to think that I'd never seen "The Big Lebowski," and was as a result treated, once again, to the sight of The Dude, interrupted by burgling nihilists while smoking dope in his bathtub, calling out, without changing comfortable position, the following complaint: "Hey, this is a private residence, man."  May he always abide.

 

Of madmen and tea partiers

According to H. R. Haldeman, his chief of staff, Richard Nixon subscribed to "the madman theory of the presidency."  The idea is that, in adversarial negotiations, you benefit if the other side has to consider the possibility that you are just crazy enough to make good on threats that would be dismissed if made by a manifestly rational actor.  The threat to use nuclear weapons, for instance, is a bit too much like a gun with two barrels, one conventional and the other curved around so that it points straight back.  One may threaten an intruder with such a weapon but it can never make sense to shoot.  A smart burglar understands this and is undeterred. 

If, on the other hand, you appear unstable and reckless, then your adversary will be more inclined to credit the threat, and will conform his behavior to your will.

One problem is that your cultivation of madness has to be thoroughgoing to be believed.  Thus the madman theory commits you to act recklessly at all times, on all matters, lest your adversary see through the ruse.  Riding this logic to the end of the line, you can see how it is best actually to be crazy, and why President Obama is at somewhat of a disadvantage when negotiating with the Republicans on such issues as the debt ceiling.  It's possible that they really would shut down the government and default on the national debt.  By the logic of the madman theory, the tea-party brigade is well-positioned to take advantage of Obama's sanity, his seriousness about governing and inclination to do whatever is necessary to avert a catastrophe.

The Casey Anthony verdict

Now that I have the attention of all eight of my readers, I want to announce my disappointment with President Obama on the gay marriage issue that I've been writing about recently--here and here, for instances.  The vote in New York forced members of its state legislature to say Yes or No.  In the state senate, which has a Republican majority, four Republican members said Yes, and the bill became law.  One of the four, Roy McDonald, memorably summarized his internal dialogue: "You get to the point where you evolve in your life where everything isn't black and white, good and bad, and you try to do the right thing. . . .  You might not like that.  You might be very cynical about that.  Well, fuck it, I don't care what you think.  I'm trying to do the right thing."

The word "evolve" plays its part in the president's pronouncements on this issue as well.  Instead of saying Yes or No, he says his position is "evolving."  From what to where?  When he had a job like Roy McDonald's, he indicated that he supported marriage equality.  Obama, however, represented liberal Hyde Park in Chicago, whereas McDonald represents a conservative district in upstate New York.  On the national stage, Obama's public position changed, and his self-described "evolving" began. 

His deployment of "evolving" is probably intended to be redolent of portentous moral deliberations occurring at the core of his noble being, where the arguments against contend with the rising arguments for.  But if we are to believe the state senator from Hyde Park, he was never persuaded by the arguments against.  It seems evident that it's not his position but his political calculations that are "evolving."

Now, "political calculation" is a term, like "rhetoric," that has an undeserved bad name.  If your line of work is politics, you had better be good at making political calculations (and being a gifted rhetorician is an advantage, too).  New York's Roy McDonald spoke also of "trying to do the right thing," a goal that cannot be conceived simply.  Hendrik Hertzberg has recently argued that Obama, had he announced his full-throated support of gay marriage a year ago, would have added "Obamarriage" to "Obamacare" and united the tea-party brigade with the Christianist hordes.  The evolution of society's views on marriage equality would have stalled.

Maybe.  Let us give Obama credit for the demise of "don't-ask-don't-tell"; also, for the decision not to defend the federal Defense of Marriage Act.  On marriage equality, though, Hertzberg sounds to me like an ingenious defense attorney who, after his client has been caught, constructs an after-the-fact "theory of the case" that strains to create reasonable doubt.  Meanwhile, Obama looks like an insincere trimmer.  Society hasn't moved toward acceptance of gay marriage on account of anything he's done.  One of his miscalculations has been to suppose that "doing the right thing" on gay marriage would be political suicide.  By now he'd probably like to endorse gay marriage but that would make him a laughingstock.  He was contemplating Reinhold Niebuhr while Roy McDonald was saying, "Fuck it, I'm doing the right thing."

Looking back at Hemingway

Fifty years ago today, Ernest Hemingway committed suicide at his home in Ketchum, Idaho.  The New Yorker has a collection of photographs of him here.  I don't want to make too much of it, but in my mind there are two Hemingways, and the photographs of him tend to fall easily into the one or the other class: there is the handsome young man, slim, disciplined, a friend to many other poor artists living in Paris in the 1920s; and then there is the over-sized, white-bearded celebrity author photographed beside some dead animals in Life.  He seems to have arrived at old age so quickly that the vigilant photographers failed to document the stages of middle-life.  Before Hemingway was 35 he had given us In Our Time, Men Without Women, Winner Take Nothing, The Sun Also Rises, and A Farewell to Arms.  If everything he wrote is of interest, that is mainly because he is the author of these five books, too.

On NPR this morning, Scott Simon described Hemingway as "a boxer, a boozer, a philanderer and a big-game hunter who wrote some of the most sublime prose of the English language:  short, sharp, piercing sentences that told stories about soldiers, lovers, hunters, bravery, fear and death."  One detects the two Hemingways in this one sentence, but I'm afraid that here, as elsewhere, the famous author overwhelms the artist.  Hemingway is one of our greatest writers but to speak of "short, sharp, piercing sentences" suggests one flight over from too high an altitude.  I don't know how exactly this distillation got going; George Will proved he's a subscriber by once comparing the "terse" style of George W Bush to Hemingway, thereby eliciting this contemptuous riposte from Norman Mailer.  Anyway, as a sample of Hemingway's "sublime prose," I offer here the opening to A Farewell to Arms:

In the late summer of that year we lived in a house in a village that looked across the river and the plain to the mountains.  In the bed of the river there were pebbles and boulders, dry and white in the sun, and the water was clear and swiftly moving and blue in the channels.  Troops went by the house and down the road and the dust they raised powdered the leaves of the trees.  The trunks of the trees too were dusty and the leaves fell early that year and we saw the troops marching along the road and the dust rising and leaves, stirred by the breeze, falling and the soldiers marching and afterward the road bare and white except for the leaves.

Read it aloud and see if you don't like the sound the words make.  The language is simultaneously poetic, charged, and simple--not one word of more than two syllables.  And the words are wedded to a theme, which is Hemingway's great theme (and that of the Book of Ecclesiastes).  In the first sentence, there are mountains; in the second, pebbles and boulders; in the third, dust; and, in the fourth, "dust" is repeated so as to achieve an almost choric effect: mountains, boulders, pebbles, dust, dust, dust.  The first mention of human activity is in the first sentence mentioning dust.